Given the root of the quadratic equation of $\displaystyle 4ax^2+bx+8=0$ are equal.Express $\displaystyle a$ in terms of $\displaystyle b$
You know the quadratic formula, don't you: $\displaystyle x= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}$
The two roots will be equal if and only if the square root is 0.
Another way to do this is to write the equation as $\displaystyle 4ax^2+ bx+ 8= 4a(x- x_0)(x- x_0)$. Multiply the right side and set corresponding coefficients equal.